Vibrating -mass gyroscope systems and method

ABSTRACT

One embodiment of the invention includes a vibrating-mass gyroscope system. A sensor system includes a substantially planar vibrating-mass including opposite first and second surfaces and electrodes that extend longitudinally in a periodic pattern across the first and/or second surfaces. The electrodes include sets of drive and sense electrodes that are capacitively coupled to respective matching sets of drive and sense electrodes associated with a housing and which are separated from and facing the respective first and second surfaces. A gyroscope controller generates a drive signal provided to one of the array of drive electrodes and the substantially matching array of drive electrodes to provide for in-plane periodic oscillatory motion of the vibrating-mass, and generates a force-rebalance signal that is provided to one of the array of sense electrodes and the substantially matching array of sense electrodes to calculate rotation of the vibrating-mass gyroscope system about an input axis.

TECHNICAL FIELD

This disclosure relates generally to sensor systems, and specifically toa vibrating-mass gyroscope systems and method.

BACKGROUND

There are a number different types of vibrating-mass gyroscope systemsthat can be configured to calculate rotation about a sensitive (e.g.,input) axis. One type of gyroscope is a Coriolis vibratory gyroscope(CVG). One example of a CVG is a tuning fork gyroscope in which twomasses (e.g. tines) can vibrate in plane along a drive axis. In responseto an applied angular rate about an input axis parallel to the tines ofthe tuning fork, Coriolis forces cause the tines to vibrate out of planealong a sense axis (e.g., 90° relative to a drive axis). The amplitudeof the out-of-plane motion in open loop instruments or the forcerequired to rebalance and null the out-of-plane motion in closed-loopinstruments can correspond to a measure of the angular rate appliedabout the input axis.

SUMMARY

One embodiment of the invention includes a vibrating-mass gyroscopesystem. A sensor system includes a substantially planar vibrating-massincluding opposite first and second surfaces and electrodes that extendlongitudinally in a periodic pattern across the first and/or secondsurfaces. The electrodes include sets of drive and sense electrodes thatare capacitively coupled to respective matching sets of drive and senseelectrodes associated with a housing and which are separated from andfacing the respective first and second surfaces. A gyroscope controllergenerates a drive signal provided to one of the array of driveelectrodes and the substantially matching array of drive electrodes toprovide for in-plane periodic oscillatory motion of the vibrating-mass,and generates a force-rebalance signal that is provided to one of thearray of sense electrodes and the substantially matching array of senseelectrodes to calculate rotation of the vibrating-mass gyroscope systemabout an input axis.

Another embodiment of the invention includes a method for calculatingrotation about an input axis in a vibrating-mass gyroscope system. Themethod includes monitoring a drive pickoff signal associated with one ofan array of drive electrodes that extend longitudinally in a periodicpattern across at least one of a first surface and a second surface of asubstantially planar vibrating-mass and a substantially matching arrayof drive electrodes that extend longitudinally in a periodic patternacross at least one of a first surface and a second surface of ahousing. The first surface of the substantially planar vibrating-masscan face the first surface of the housing and the second surface of thesubstantially planar vibrating-mass faces the second surface of thehousing. The method also includes providing a drive signal to the one ofthe array of drive electrodes of the substantially planar vibrating-massand the substantially matching array of drive electrodes of the housingbased on the drive pickoff signal to provide an in-plane periodicoscillatory motion of the substantially planar vibrating-mass. Themethod also includes monitoring a force-rebalance pickoff signalassociated with one of an array of sense electrodes that extendlongitudinally in a periodic pattern across at least one of the firstand second surfaces of the substantially planar vibrating-mass and asubstantially matching array of sense electrodes that extendlongitudinally in a periodic pattern across at least one of the firstand second surfaces of the housing. The method further includesproviding a force-rebalance signal to the one of the array of senseelectrodes of the substantially planar vibrating-mass and thesubstantially matching array of sense electrodes of the housing based onthe force-rebalance pickoff signal to calculate a rotation of thevibrating-mass gyroscope system about an input axis.

Another embodiment of the invention includes a vibrating-mass gyroscopesystem. The system includes a sensor system comprising a plurality ofsubstantially planar vibrating-masses that each comprise a firstsurface, a second surface opposite the first surface, and a plurality ofelectrodes that extend longitudinally in a periodic pattern across eachof the first and second surfaces. The plurality of electrodes caninclude an array of drive electrodes and an array of sense electrodesthat are capacitively coupled to a substantially matching array of driveelectrodes and a substantially matching array of sense electrodes,respectively, associated with a housing and which are separated from andfacing the respective at least one of the first and second surfaces ofeach of the plurality of vibrating-masses. The system also includes agyroscope controller configured to generate a drive signal that isprovided to one of the array of drive electrodes and the substantiallymatching array of drive electrodes associated with each of the pluralityof vibrating-masses to provide for an in-plane periodic oscillatorymotion of each of the plurality of substantially planarvibrating-masses. The gyroscope controller also generates aforce-rebalance signal that is provided to one of the array of senseelectrodes and the substantially matching array of sense electrodesassociated with each of the plurality of vibrating-masses to calculate arotation of the vibrating-mass gyroscope system about an input axis.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example of a vibrating-mass gyroscope system.

FIG. 2 illustrates an example of a sensor system.

FIG. 3 illustrates an example of a vibrating-mass.

FIG. 4 illustrates another example of a sensor system.

FIG. 5 illustrates an example of a quad-mass sensor system.

FIG. 6 illustrates another example of a vibrating-mass.

FIG. 7 illustrates an example of a method for calculating rotation aboutan input axis in a vibrating-mass gyroscope system.

DETAILED DESCRIPTION

This disclosure relates generally to sensor systems, and specifically toa vibrating-mass gyroscope systems and method. The vibrating-massgyroscope system includes a sensor system and a gyroscope controller.The sensor system can include at least one vibrating-mass that isarranged as a substantially planar vibrating-mass having a first surfaceand a second surface opposite the first surface. The vibrating-mass(es)can include an array of drive electrodes and an array of senseelectrodes that extend longitudinally in a periodic pattern across atleast one of the first and second surfaces of the vibrating-mass(es). Asan example, the drive electrodes and the sense electrodes can extend inorthogonal directions with respect to each other, and can be arranged onthe same surface (e.g., both surfaces) of the vibrating-masses withrespect to each other. The sensor system can also include a housing thatincludes respective matching arrays of drive electrodes and senseelectrodes that are arranged on respective surfaces of the housingfacing the vibrating-mass(es), such that the matching arrays ofelectrodes can be capacitively coupled with the arrays of driveelectrodes and sense electrodes associated with the vibrating-mass(es).

The gyroscope controller can be configured to generate a drive signaland a force-rebalance signal that are provided to the arrays of driveelectrodes and sense electrodes, respectively, associated with thevibrating-mass(es) and the housing. For example, the respective signalscan be provided to the electrodes on the housing while the electrodes onthe vibrating-mass(es) are electrically coupled to a bias voltage. Thedrive signal can thus provide an electrostatic force that induces anin-plane periodic oscillatory motion of the vibrating-mass(es), such asat a frequency that is approximately equal to a resonant frequency of avibrating-mass spring system that is coupled to the housing (e.g., lessthan 50 kHz). As an example, the in-plane periodic oscillatory motioncan be 180° out-of-phase with respect to a given pair ofvibrating-masses. The force-rebalance signal can likewise provide anelectrostatic force to provide a force-rebalance of thevibrating-mass(es) in response to rotation of the sensor system about aninput axis. As an example, the electrostatic force for force-rebalanceof the vibrating-mass(es) can be orthogonal with respect to the in-planeperiodic oscillatory motion provided by the drive signal. A magnitude ofthe force-rebalance signal, and thus the electrostatic force, that isrequired to maintain the vibrating-mass(es) at a null position of apickoff along a sense axis can correspond to a combination of a rate ofrotation of the sensor system about the input axis and gyroscope bias.Therefore, the magnitude of the force-rebalance signal can beimplemented by the gyroscope controller (e.g., an associated inertialsensor processor) to calculate the angular rotation of the sensor systemabout the input axis (e.g., upon compensation of gyroscope bias).

FIG. 1 illustrates an example of a vibrating-mass gyroscope system 10.The vibrating-mass gyroscope system 10 can be implemented in any of avariety of applications with which accurate measurement of rotation maybe necessary, such as aerospace and nautical navigation. Thevibrating-mass gyroscope system 10 includes a sensor system 12 and agyroscope controller 14.

The sensor system 12 includes at least one vibrating-mass 16 that isarranged as a substantially planar inertial mass. As an example, thevibrating-mass(es) 16 can be arranged as an even-number quantity (e.g.,four) of vibrating-masses. For example, the vibrating-mass(es) 16 can befabricated as a layer of silicon. The sensor system 12 also includes ahousing 18 that can envelope the vibrating-mass(es) 16, such asincluding a layer above the vibrating-mass(es) 16 and a layer below thevibrating-mass(es) 16. As an example, each of the vibrating-mass(es) 16can be coupled to the housing 18 via spring-mass systems (e.g.,flexures) that can allow for in-plane motion of the vibrating-mass(es)16 in orthogonal directions. In the example of FIG. 1, thevibrating-mass(es) 16 can each include an array of drive electrodes 20and an array of sense electrodes 22, and the housing 18 includes anarray of drive electrodes 24 and an array of sense electrodes 26, witheach array being associated with a respective one of thevibrating-mass(es) 16. Each of the arrays of drive electrodes 20 andsense electrodes 22 can be arranged on at least one of a first surface(e.g., a top surface) and a second surface (e.g., a bottom surface)opposite the first surface. Similarly, each of the arrays of driveelectrodes 24 and sense electrodes 26 can be arranged on at least one ofa first surface (e.g., a top surface) that faces the first surface ofthe vibrating-mass(es) 16 and a second surface (e.g., a bottom surface)that faces the second surface of the vibrating-mass(es) 16. Therefore,the drive electrodes 20 and the drive electrodes 24 can be capacitivelycoupled with respect to each other, and the drive electrodes 22 and thedrive electrodes 26 can be capacitively coupled with respect to eachother.

The gyroscope controller 14 is configured to generate drive signals DRVthat are provided to at least one of the arrays of drive electrodes 20and 24 to generate electrostatic force to provide an in-plane periodicoscillatory motion of the vibrating-mass(es) 16. For example, the drivesignals DRV can have a frequency that is approximately equal to aresonant frequency associated with one or more springs and thevibrating-mass(es) 16 that is coupled to the housing 18. As an example,in the example of plural vibrating-masses 16, the in-plane periodicoscillatory motion can be provided at 180° out-of-phase with respect toeach given pair of vibrating-masses to provide counter-balanced motionof the vibrating-mass(es) 16. The gyroscope controller 14 is alsoconfigured to generate force-rebalance signals FRB that are provided toat least one of the arrays of sense electrodes 22 and 26 to generateelectrostatic force to null the sense pickoff and the motion of thevibrating-mass(es) 16 in response to rotation of the sensor system 12about an input axis and gyroscope bias. For example, the force-rebalancesignals FRB can have a frequency that is approximately equal to thefrequency of the drive signals DRV (e.g., approximately equal to theresonant frequency).

The drive signals DRV and the force-rebalance signals FRB can begenerated at an amplitude that is based on demodulated pickoffsignal(s). The demodulated pickoff signals PO can have a frequency thatis significantly greater than the frequency of the force-rebalancesignals FRB (e.g., an order of magnitude or greater). As an example, thesense electrodes 22 and 26 can be arranged in a periodic array thatextend longitudinally and orthogonally with respect to a longitudinalextension of the respective drive electrodes 20 and 24. Therefore,rotation of the sensor system 12 about the input axis can result inmotion of the vibrating-mass(es) 16 orthogonally with respect to thein-plane periodic oscillatory motion associated with the driveelectrodes 20 and 24. Accordingly, the electrostatic force that isgenerated by the sense electrodes 22 and 26 in response to theforce-rebalance signals FRB can force the vibrating-mass(es) 16 to bemaintained at a null position along a sense axis. As described herein,the term “null position” corresponds to a position of thevibrating-mass(es) 16 along the sense axis corresponding to anapproximate zero value associated with the demodulated pickoffsignal(s).

The gyroscope controller 14 includes a processor 28, a signal generator30, and a demodulator system 32. The signal generator 30 is configuredto generate the drive signals DRV that are provided to the driveelectrodes 20 and/or 24 and the force-rebalance signals FRB that areprovided to the sense electrodes 22 and/or 26. In response to theapplication of the drive signals DRV and the force-rebalance signalsFRB, pickoff signals PO are provided to the demodulator system 32. As anexample, the pickoff signals PO can correspond to amplitude-modulatedpickoff signals that are capacitively coupled to the drive electrodes 20and 24 and/or the sense electrodes 22 and 26 in response to motion ofthe vibrating mass(es) 16. The pickoff signals PO can thus bedemodulated via the demodulator system 32 to determine an appropriatemagnitude of the respective drive signals DRV and force-rebalancesignals FRB, such as to maintain the in-plane periodic oscillatorymotion of the vibrating-mass(es) 16 and to maintain thevibrating-mass(es) 16 in the null position in the sense axis,respectively.

Thus, the processor 28 can calculate the magnitude of theforce-rebalance signals FRB in a manner that is indicative of the rateof angular rotation of the sensor system 12 about the input axis andgyroscope bias. As an example, a magnitude of the force-rebalancesignal, and thus the electrostatic force, that is required to maintainthe vibrating-mass(es) 16 at the null position along the sense axis cancorrespond to a rate of rotation of the sensor system 12 about the inputaxis (e.g., including a gyroscope bias). Therefore, the magnitude of theforce-rebalance signals FRB can be implemented by the processor 28 tocalculate the angular rotation of the sensor system 12 about the inputaxis, such as after compensating for the gyroscope bias. Accordingly,the gyroscope controller 14 can provide the measurement of the angularrate of rotation about the input axis as an output signal ROT. As anadditional example, the drive electrodes 20 and 24 and the senseelectrodes 22 and 26 can be interchangeable with respect to the drivesignals DRV and the force-rebalance signals FRB to provide mode reversalfor self-calibration of the gyroscope bias.

FIG. 2 illustrates an example of a sensor system 50. The sensor system50 is demonstrated in the example of FIG. 2 in a first view 51 and asecond view 52 based on a Cartesian coordinate system 53, such that thesecond view 52 is rotated 90° about the Y-axis relative to the firstview 51 (i.e., right-hand rotated about the −Y direction). The sensorsystem 50 can correspond to the sensor system 12 in the example ofFIG. 1. Therefore, reference is to be made to the example of FIG. 1 inthe following description of the example of FIG. 2.

The sensor system 50 includes a first cover layer 54, a vibrating-mass56, and a second cover layer 58. In the example of FIG. 2, thevibrating-mass 56 is demonstrated as substantially planar, with thefirst cover layer 54 being provided as a layer above the vibrating-mass56 and the second cover layer 58 being provided as a layer below thevibrating-mass 56. As an example, the vibrating-mass 56 can be a layerof etched silicon, and the first and second cover layers 54 and 58 caneach be formed from etched silicon-on-insulator (SOI) layers. The firstcover layer 54 and the second cover layer 58 can collectively form partof the housing 18 to which the vibrating-mass 56 can be coupled viaspring-mass systems (not shown) to allow for in-plane motion of thevibrating-mass 56 relative to the first and second cover layers 54 and58 in an X-Z plane, as demonstrated by the Cartesian coordinate system53.

In the example of FIG. 2, the vibrating-mass 56 includes a first arrayof drive electrodes 60 and a first array of sense electrodes 62 that aredisposed on a top surface of the substantially planar vibrating-mass 56,and includes a second array of drive electrodes 64 and a second array ofsense electrodes 66 that are disposed on a bottom surface of thesubstantially planar vibrating-mass 56 opposite the top surface. Thedrive electrodes 60 and 64 and the sense electrodes 62 and 66 eachextend longitudinally across the respective top and bottom surfaces ofthe vibrating-mass 56 in a manner such that the drive electrodes 60 and64 extend along the Z-axis and the sense electrodes 62 and 66 extendalong the X-axis, and thus orthogonally with respect to the driveelectrodes 60 and 64. Similarly, the first cover layer 54 includes anarray of drive electrodes 68 and an array of sense electrodes 70 thatare disposed on a surface facing the top surface of the substantiallyplanar vibrating-mass 56, and the second cover layer 58 includes anarray of drive electrodes 72 and an array of sense electrodes 74 thatare disposed on a surface facing the bottom surface of the substantiallyplanar vibrating-mass 56.

The arrays of drive electrodes 68 and 72 and the arrays of senseelectrodes 70 and 74 can be arranged as substantially matching therespective arrays of drive electrodes 60 and 64 and sense electrodes 62and 66, such as based on dimensions, quantity, and general arrangement.The drive electrodes 60 and sense electrodes 62 can be separated fromthe respective matching drive electrodes 68 and 70 by a distance “D”(e.g., approximately 2 μm), and the drive electrodes 64 and senseelectrodes 66 can be separated from the respective matching driveelectrodes 72 and 74 by the distance “D”. In the example of FIG. 2, thevibrating-mass 56 is demonstrated as being at a rest state (e.g.,mechanical spring forces that are acting upon the vibrating-mass 56 aresubstantially equal and opposite). The arrays of drive electrodes 68 and72 and the arrays of sense electrodes 70 and 74 are demonstrated assubstantially off-alignment with respect to the respective matchingarrays of drive electrodes 60 and 64 and sense electrodes 62 and 66. Thedrive electrodes 60 and sense electrodes 62 can be capacitively coupledto the respective matching drive electrodes 68 and 70, and the driveelectrodes 64 and sense electrodes 66 can be capacitively coupled to therespective matching drive electrodes 72 and 74 based on an amount ofoverlap of the respective electrodes along a Y-axis, such as in responseto rotation about an input axis that can be parallel to the Y-axis.Accordingly, the electrostatic force can be a modulated attractive forcewith respect to the matching sets of electrodes to provide for aperiodic oscillatory motion and a force-rebalance, as described ingreater detail herein.

FIG. 3 illustrates an example of a vibrating-mass 100. Thevibrating-mass 100 can correspond to the vibrating-mass 56 demonstratedin the example of FIG. 2, such as from an overhead view along the Y-axisof the Cartesian coordinate system 58. Thus, the vibrating-mass 100 isdemonstrated in the example of FIG. 3 in a view of either the topsurface or the bottom surface of the vibrating-mass 100. Thevibrating-mass 100 includes an array of drive electrodes 102 and anarray of sense electrodes 104. The drive electrodes 102 and the senseelectrodes 104 each extend longitudinally across the surface of thevibrating-mass 100 in a manner such that the drive electrodes 102 extendalong the Z-axis and the sense electrodes 104 extend along the X-axis,and thus orthogonally with respect to the drive electrodes 102. As anexample, the opposite surface of the substantially planar vibrating-mass100 can likewise include a substantially similar (e.g., equal)arrangement of drive electrodes and sense electrodes. In the example ofFIG. 3, the array of drive electrodes 102 and the array of senseelectrodes 104 each occupy approximately half of the area of thevibrating-mass 100. However, it is to be understood that one of thearrays of drive electrodes 102 and force-rebalance 104 can occupy arelatively larger area of the surface of the vibrating-mass 100.Additionally, it is also to be understood that the designation of thedrive electrodes 102 and force-rebalance electrodes 104 can beinterchangeable consistent with the arrangement of respective electrodeson the opposing surfaces.

As described previously, the vibrating-mass 100 can correspond to thevibrating-mass 56, and can thus be arranged between the first and secondcover layers 54 and 58. As an example, the first and second cover layers54 and 58 can thus each include arrays of drive electrodes and senseelectrodes that substantially match the arrays of drive electrodes 102and sense electrodes 104. As also described previously, the arrangementof the arrays of drive electrodes 102 and sense electrodes 104 can besuch that the arrays of drive electrodes 102 and sense electrodes 104can be unaligned (e.g., laterally offset) with respect to the matchingelectrodes on the first and second cover layers 54 and 58 in a reststate. Therefore, in response to the drive signal DRV, an electrostaticforce can be generated between the drive electrodes 102 and thesubstantially matching drive electrodes associated with the respectivehousing to provide for periodic oscillatory movement of thevibrating-mass 100 in the X-Z plane, and specifically along the X-axiscorresponding to a drive axis (“DRV”). Similarly, in response to theforce-rebalance signal FRB, an electrostatic force can be generatedbetween the sense electrodes 104 and the substantially matching driveelectrodes associated with the respective housing to provideforce-rebalance of the vibrating-mass in response to movement of thevibrating-mass 100 in the X-Z plane, and specifically along the Z-axiscorresponding to a sense axis (“SNS”).

As an example, the drive electrodes 102 and the sense electrodes 104 canbe separate by gaps that are approximately 25 μm wide and approximately50 μm deep. The drive electrodes 102 can have a length of approximately1400 μm, and the sense electrodes 104 can have a length of approximately2800 μm. Therefore, the sense electrodes 104 can have a length that isapproximately twice the length of the drive electrodes 102. However,based on the orthogonal arrangement of the drive and sense electrodes102 and 104 and that the drive and sense electrodes 102 and 104 eachoccupy approximately half the area of the surface of the vibrating-mass100, the quantity of drive electrodes 102 can be approximately doublethe quantity of the sense electrodes 104. Therefore, the driveelectrodes 102 and the sense electrodes 104 can each have anapproximately equal electrostatic force in response to an approximatelyvoltage stimulus, and can exhibit a substantially equal capacitance.Such an arrangement of the drive electrodes 102 and sense electrodes 104with respect to the capacitive coupling to the respective electrodes ofthe housing can result in significant performance improvement overtypical variable area electrostatic forcer systems for forcing anddetecting motion (e.g., “comb” drive systems).

FIG. 4 illustrates another example of a sensor system 150. The sensorsystem 150 can correspond to the sensor system 12 in the example of FIG.1 and/or the sensor system 50 in the example of FIG. 2. As an example,the sensor system 150 can correspond to the sensor system 50. Therefore,reference is to be made to the example of FIGS. 1 and 2 in the followingdescription of the example of FIG. 3.

The sensor system 150 includes a first cover layer 152, a vibrating-mass154, and a second cover layer 156. In the example of FIG. 2, thevibrating-mass 154 is demonstrated as substantially planar, with thefirst cover layer 152 being provided as a layer above the vibrating-mass154 and the second cover layer 156 being provided as a layer below thevibrating-mass 154. As an example, the vibrating-mass 154 can be a layerof etched silicon, and the first and second cover layers 152 and 156 caneach be formed from etched silicon-on-insulator (SOI) layers. The firstcover layer 152 and the second cover layer 156 can collectively formpart of the housing 18 to which the vibrating-mass 154 can be coupledvia spring-mass systems (not shown) to allow for in-plane motion of thevibrating-mass 154 relative to the first and second cover layers 152 and156, as described previously.

In the example of FIG. 4, the vibrating-mass 154 includes a first arrayof drive electrodes 160 and a second array of drive electrodes 162 thatare disposed on top and bottom surfaces of the substantially planarvibrating-mass 154. Similarly, the first cover layer 152 includes anarray of drive electrodes 164 that are disposed on a surface facing thefirst array of drive electrodes 160, and the second cover layer 156includes an array of drive electrodes 166 that are disposed on a surfacefacing the second array of drive electrodes 162. In addition, the firstcover layer 152, the vibrating-mass 154, and the second cover layer 156can each include an array of sense electrodes, similar to as describedpreviously (e.g., with the vibrating-mass including an array on both thetop surface and the bottom surface). For example, the sense electrodescan extend longitudinally in orthogonal directions with respect to thedrive electrodes 160, 162, 164, and 166, respectively.

Similar to as described previously, the drive electrodes 160 can bearranged as substantially matching the respective array of driveelectrodes 164, and the drive electrodes 162 can be arranged assubstantially matching the respective array of drive electrodes 166,such as based on dimensions, quantity, and general arrangement. Thedrive electrodes 160 and 164 and the drive electrodes 162 and 166 can berespectively separated by a distance “D” (e.g., approximately 2 μm). Asdemonstrated in the example of FIG. 4, the substantially matching setsof drive electrodes 160 and 164 and drive electrodes 162 and 166 aredemonstrated as unaligned (e.g., laterally offset) in a rest state ofthe vibrating-mass 154. Therefore, the drive electrodes 160 and 164 andthe drive electrodes 162 and 166 can be capacitively coupled based on anamount of overlap of the respective electrodes along the Y-axis. In theexample of FIG. 4, the first cover layer 152 receives a first drivesignal DRV₁ and a first force-rebalance signal FRB₁, and the secondcover layer 156 receives a second drive signal DRV₂ and a secondforce-rebalance signal FRB₂. As an example, the first and second drivesignals DRV₁ and DRV₂ can correspond to the same signal and the firstand second force-rebalance signals FRB₁ and FRB₂ can correspond to thesame signal.

The vibrating-mass 154 is demonstrated as being coupled to apredetermined bias voltage V_(B), which can thus allow for a sinusoidalattractive electrostatic force to act upon the vibrating-mass 154 inresponse to the first and second drive signals DRV₁ and DRV₂ and thefirst and second force-rebalance signals FRB₁ and FRB₂. While the biasvoltage V_(B) is demonstrated as being coupled to the vibrating-mass154, it is to be understood that the bias voltage V_(B) can instead becoupled to the first and second cover layers 152 and 156. Therefore, thefirst and second drive signals DRV₁ and DRV₂ can generate theelectrostatic force to provide for the in-plane periodic oscillatorymotion of the vibrating-mass 154 along the drive axis and the first andsecond force-rebalance signals FRB₁ and FRB₂ can generate theelectrostatic force to maintain the vibrating-mass 154 in the nullposition along the sense axis in response to rotation of the sensorsystem 150 about the input axis. As an example, each of the first andsecond drive signals DRV₁ and DRV₂ and the first and secondforce-rebalance signals FRB₁ and FRB₂ can have a frequency that isapproximately equal to a resonant frequency of the vibrating-mass 154.Additionally, a carrier signal CA is provided to the vibrating-mass 154.As an example, the carrier signal CA can be generated by the gyroscopecontroller 14 as an AC voltage having a frequency that is significantlygreater than the resonant frequency of the vibrating-mass (e.g.,approximately 200 kHz or more). Thus, the carrier signal CA is summedwith the predetermined bias voltage V_(B).

The gyroscope controller 14 can monitor a capacitance associated with ancapacitive coupling between the drive electrodes 160 and 164,demonstrated as a signal D_PO₁, and a capacitance associated with ancapacitive coupling between the drive electrodes 162 and 166,demonstrated as a signal D_PO₂. Similarly, the gyroscope controller 14can monitor a capacitance associated with an capacitive coupling betweenthe sense electrodes associated with the vibrating-mass 154 and thefirst cover layer 152 (e.g., the sense electrodes 62 and 70 in theexample of FIG. 2), demonstrated as a signal F_PO₁, and a capacitanceassociated with an capacitive coupling between the sense electrodesassociated with the vibrating-mass 154 and the second cover layer 156(e.g., the sense electrodes 66 and 74 in the example of FIG. 2),demonstrated as a signal F_PO₂. The signals D_PO₁, D_PO₂, F_PO₁, andF_PO₂ can collectively correspond to the pickoff signals PO in theexample of FIG. 1. In response, the gyroscope controller 14 cancalculate the magnitude of the first and second drive signals DRV₁ andDRV₂ required to maintain the in-plane periodic oscillatory motion ofthe vibrating-mass 154 along the drive axis, and to calculate themagnitude of the first and second force-rebalance signals FRB₁ and FRB₂to maintain the vibrating-mass 154 in the null position along the senseaxis.

As an example, the gyroscope controller 14 can be configured todemodulate the signals D_PO₁, D_PO₂, F_PO₁, and F_PO₂ at the frequencyof the carrier signal CA, such that the demodulated signals D_PO₁,D_PO₂, F_PO₁, and F_PO₂ will have an amplitude that is modulated atapproximately the resonant frequency of the vibrating-mass 154 based onthe periodic oscillatory motion, angular rotation about the input axis,and/or quadrature effects resulting from a difference in the resonancefrequency between the two principle elastic axes. Thus, the gyroscopecontroller 14 can provide the first and second drive signals DRV₁ andDRV₂ at an amplitude required to maintain the periodic motion of thevibrating-mass 154 along the drive axis. The gyroscope controller 14 canalso provide the first and second force-rebalance signals FRB₁ and FRB₂at an amplitude required to maintain the vibrating-mass 154 at a nullposition along the sense axis, and to substantially mitigate quadratureeffects that are exhibited approximately 90° out-of-phase of the angularrotation effects, as provided in the signals F_PO₁, and F_PO₂ (e.g.,sine and cosine, respectively). Additionally, because the magnitude ofthe first and second force-rebalance signals FRB₁ and FRB₂ can beproportional to the movement of the vibrating-mass 154 along the senseaxis in response to rotation about the input axis, the gyroscopecontroller 14 can calculate the rotation about the input axis ROT basedon the calculated magnitude of the first and second force-rebalancesignals FRB₁ and FRB₂ (e.g., in response to the angular rotationmodulation on the signals F_PO₁, and F_PO₂).

Based on the arrangement of electrodes 160, 162, 164, and 166, thesensor system 150 can achieve a significant performance improvement overother typical force-rebalance systems that implement motion detectionvia capacitive coupling, such as those that implement electrodes thatare move to change an overlapping interdigitation with respect toopposing electrodes (i.e., a “comb” drive configuration). For example,because the electrodes 160, 162, 164, and 166 have a significantlygreater area of overlap and smaller gap distance relative to “comb”drive architectures, the sensor system 150 can achieve significantlygreater forcing capability and capacitance relative to “comb” drivearchitectures. In addition, the vibrating-mass 154 can have asignificantly greater mass than moving elements in other motion sensingapplications (e.g., the “comb” drive architecture), and because theelectrodes 160 and 162 can be disposed on opposing surfaces of thevibrating-mass 154, the distance “D” can be very small based on theelectrostatic forces being applied substantially equally and oppositelyon both surfaces of the vibrating-mass 154. Therefore, for all of thesereasons, the associated sensor system (e.g., the sensor system 10) cancalculate the angular rotation ROT at a significantly improvedsignal-to-noise ratio (SNR) relative to typical other motion sensingapplications.

FIG. 5 illustrates an example of a quad-mass sensor system 200. Thequad-mass sensor system 200 can correspond to the sensor system 12 inthe example of FIG. 1. Therefore, reference is to be made to the exampleof FIG. 1 in the following description of the example of FIG. 5.

The quad-mass sensor system 200 includes a first vibrating-mass 202, asecond vibrating-mass 204, a third vibrating-mass 206, and a fourthvibrating-mass 208 that are arranged in pairs. In the example of FIG. 5,the first vibrating-mass 202 and the second vibrating-mass 204 are afirst pair of vibrating-masses that are arranged substantially the samebut implement motion in opposite directions with respect to each other,and the third vibrating-mass 206 and the fourth vibrating-mass 208 are asecond pair of vibrating-masses that are arranged substantially the samebut implement motion in opposite directions with respect to each otherand 180° out-of-phase with the first and second vibrating masses 202 and204. For example, the first and second vibrating-masses 202 and 204 caneach be configured substantially similar to the vibrating-mass 100 inthe example of FIG. 3, and can thus each include an array of driveelectrodes 210 and an array of sense electrodes 212.

In response to one or two respective drive signals DRV, the first andsecond vibrating-masses 202 and 204 can be configured to move in anin-plane periodic oscillatory manner in opposite directions along thedrive axis at a given time, such as 180° out-of-phase with respect toeach other. Additionally, in response to one or two respectiveforce-rebalance signals FRB, the first and second vibrating-masses 202and 204 can be configured to maintain a null position along the senseaxis based on an electrostatic force that is applied in oppositedirections at a given time, such as 180° out-of-phase with respect toeach other. Similarly, in response to the drive signal(s) DRV, the thirdand fourth vibrating-masses 206 and 208 can be configured to move in thein-plane periodic oscillatory manner in opposite directions along thedrive axis at a given time, such as 180° out-of-phase with respect toeach other.

Additionally, in response to one or two respective force-rebalancesignals FRB, the first and second vibrating-masses 202 and 204 can beconfigured to maintain a null position along the sense axis based on anelectrostatic force that is applied in opposite directions at a giventime, such as 180° out-of-phase with respect to each other. Thus, thefirst vibrating-mass 202 is in-phase with the fourth vibrating-mass 208and out-of-phase with respect to the second and third vibrating-masses204 and 206, and the second vibrating-mass 204 is in-phase with thethird vibrating-mass 206 and out-of-phase with respect to the first andfourth vibrating-masses 202 and 208. Accordingly, based on the opposingmotion of the vibrating-masses 202, 204, 206, and 208, the sensor system200 can be substantially balanced about the input axis passing throughan approximate center 210 of the sensor system 200 at a given time.

FIG. 6 illustrates another example of a vibrating-mass 250. Thevibrating-mass 250 can correspond to the vibrating-mass 56 demonstratedin the example of FIG. 2, such as from an overhead view along the Y-axisof the Cartesian coordinate system 253. Thus, the vibrating-mass 250 isdemonstrated in the example of FIG. 6 in a view of either the topsurface or the bottom surface of the vibrating-mass 250. Thevibrating-mass 250 includes an array of drive electrodes 252 and anarray of sense electrodes 254. The drive electrodes 252 and the senseelectrodes 254 each extend longitudinally across the surface of thevibrating-mass 250 in a manner such that the drive electrodes 252 extendalong the Z-axis and the sense electrodes 254 extend along the X-axis,and thus orthogonally with respect to the drive electrodes 252.

Additionally, the vibrating-mass 250 further includes an array ofquadrature electrodes 256 that are arranged at approximately 45° withrespect to both the drive electrodes 252 and the sense electrodes 254.The quadrature electrodes 256 can have dimensions that are approximatelysimilar to the dimensions of both the drive electrodes 252 and the senseelectrodes 254 with respect to width, depth, and interposing gap width,similar to as described previously with respect to the vibrating-mass100 in the example of FIG. 3. As an example, the opposite surface of thesubstantially planar vibrating-mass 250 can likewise include asubstantially similar (e.g., equal) arrangement of drive,force-rebalance, and quadrature electrodes (e.g., laterally offset in arest state of the vibrating-mass 250). In the example of FIG. 6, thearray of quadrature electrodes 256 occupy an approximately center of thearea of the vibrating-mass 250. However, it is to be understood that thearray of quadrature electrodes 256 can be arranged in a variety oflocations on the surface of the vibrating-mass 250.

As described previously, the vibrating-mass 250 can correspond to thevibrating-mass 56, and can thus be arranged between the first and secondcover layers 54 and 58. As an example, the first and second cover layers54 and 58 can thus each include arrays of drive and force-rebalance thatsubstantially match the arrays of drive electrodes 252 and senseelectrodes 254. Therefore, in response to the drive signal DRV, anelectrostatic force can be generated between the drive electrodes 252and the substantially matching drive electrodes associated with therespective housing to provide for periodic oscillatory movement of thevibrating-mass 250 in the X-Z plane, and specifically along the X-axiscorresponding to a drive axis (“DRV”). Similarly, in response to theforce-rebalance signal FRB, an electrostatic force can be generatedbetween the sense electrodes 254 and the substantially matching driveelectrodes associated with the respective housing to provideforce-rebalance of the vibrating-mass in response to movement of thevibrating-mass 250 in the X-Z plane, and specifically along the Y-axiscorresponding to a sense axis (“SNS”).

In addition, the first and second cover layers 54 and 58 can eachinclude an array of quadrature electrodes that each substantially matchthe array of quadrature electrodes 256 (e.g., with an approximatelyequal orientation and angle to substantially optimize an overlap of thequadrature electrodes 256 with the substantially matching quadratureelectrodes along the Y-axis). Furthermore, the gyroscope controller 14can be configured to generate a DC quadrature signal. As an example, thequadrature signal can be applied to the substantially matchingquadrature electrodes on the first and second cover layers 54 and 58,such that the vibrating-mass 250 is coupled to the predetermined biasvoltage V_(B). The DC quadrature signal can thus provide a DCelectrostatic negative spring force along the angle of the quadratureelectrodes 256 in the X-Z plane to substantially match the resonantfrequencies in the two principle elastic axes and to counteractquadrature effects that can couple into the force-rebalance signal FRB.Thus, for a vibrating-mass gyroscope that implements the vibrating-mass250 in the example of FIG. 6, the gyroscope controller 14 does not needto provide sine amplitude modulation in the force-rebalance signals FRB₁and FRB₂ to substantially mitigate quadrature effects. DC quadraturecontrol can thus minimize error in the calculation of input angular rateROT due to the coupling of quadrature effects into the angular ratechannel.

For example, fabrication and electronic variations can result in changesin the separation of the resonant frequencies of the drive axis DRV andsense axis SNS of the vibrating-mass 250 due to variation of springstiffness and mass of the vibrating mass 250. As a result of suchfrequency separation, a remodulation phase error can couple quadratureeffects into the sense axis, and thus affect the magnitude of thegenerated force-rebalance signal FRB. Because the magnitude of theforce-rebalance signal FRB can correspond to rotation of the sensorsystem 50 about the input axis, such quadrature coupling can createerrors in the calculation of the rotation about the input axis ROT.Accordingly, the negative electrostatic spring force that is generatedby the DC quadrature signal with respect to the quadrature electrodes256 can substantially mitigate the quadrature motion, and thus thequadrature coupling into the force-rebalance signal FRB. As a result,the application of the DC quadrature signal with respect to thequadrature electrodes can substantially mitigate quadrature-based errorsin the calculation of the rotation about the input axis ROT.

In view of the foregoing structural and functional features describedabove, a methodology in accordance with various aspects of the presentinvention will be better appreciated with reference to FIG. 7. While,for purposes of simplicity of explanation, the methodology of FIG. 7 isshown and described as executing serially, it is to be understood andappreciated that the present invention is not limited by the illustratedorder, as some aspects could, in accordance with the present invention,occur in different orders and/or concurrently with other aspects fromthat shown and described herein. Moreover, not all illustrated featuresmay be required to implement a methodology in accordance with an aspectof the present invention.

FIG. 7 illustrates an example of a method 300 for calculating rotationabout an input axis in a vibrating-mass gyroscope system (e.g., thevibrating-mass gyroscope system 10). At 302, a drive pickoff signal(e.g., the drive pickoff signal D_PO) associated with one of an array ofdrive electrodes (e.g., the drive electrodes 60 and 64) that extendlongitudinally in a periodic pattern across at least one of a firstsurface and a second surface of a substantially planar vibrating-mass(e.g., the vibrating-mass 56) and a substantially matching array ofdrive electrodes (e.g., the drive electrodes 68 and 72) that extendlongitudinally in a periodic pattern across at least one of a firstsurface and a second surface of a housing is monitored. The firstsurface of the substantially planar vibrating-mass faces the firstsurface of the housing and the second surface of the substantiallyplanar vibrating-mass faces the second surface of the housing (e.g.,including the first and second cover layers 54 and 58). At 304, a drivesignal (e.g., the drive signal DRV) is provided to the one of the arrayof drive electrodes of the substantially planar vibrating-mass and thesubstantially matching array of drive electrodes of the housing based onthe drive pickoff signal to provide an in-plane periodic oscillatorymotion of the substantially planar vibrating-mass (e.g., in the X-Zplane). At 306, a force-rebalance pickoff signal (e.g., theforce-rebalance pickoff signal F_PO) associated with one of an array ofsense electrodes (e.g., the sense electrodes 62 and 68) that extendlongitudinally in a periodic pattern across at least one of the firstand second surfaces of the substantially planar vibrating-mass and asubstantially matching array of sense electrodes (e.g., the senseelectrodes 70 and 74) that extend longitudinally in a periodic patternacross at least one of the first and second surfaces of the housing. At308, a force-rebalance signal (e.g., the force-rebalance signal FRB) isprovided to the one of the array of sense electrodes of thesubstantially planar vibrating-mass and the substantially matching arrayof sense electrodes based on the force-rebalance pickoff signal of thehousing to calculate a rotation of the vibrating-mass gyroscope systemabout an input axis (e.g., the rotation ROT).

What have been described above are examples of the present invention. Itis, of course, not possible to describe every conceivable combination ofcomponents or methodologies for purposes of describing the presentinvention, but one of ordinary skill in the art will recognize that manyfurther combinations and permutations of the present invention arepossible. Accordingly, the present invention is intended to embrace allsuch alterations, modifications and variations that fall within thespirit and scope of the appended claims.

What is claimed is:
 1. A vibrating-mass gyroscope system comprising: asensor system comprising a substantially planar vibrating-masscomprising a first surface, a second surface opposite the first surface,and a plurality of electrodes that extend longitudinally in a periodicpattern across at least one of the first and second surfaces, theplurality of electrodes comprising an array of drive electrodes and anarray of sense electrodes that are capacitively coupled to asubstantially matching array of drive electrodes and a substantiallymatching array of sense electrodes, respectively, associated with ahousing and which are separated from and facing the respective at leastone of the first and second surfaces; and a gyroscope controllerconfigured to generate a drive signal that is provided to one of thearray of drive electrodes and the substantially matching array of driveelectrodes to provide for an in-plane periodic oscillatory motion of thesubstantially planar vibrating-mass, and to generate a force-rebalancesignal that is provided to one of the array of sense electrodes and thesubstantially matching array of sense electrodes to calculate a rotationof the vibrating-mass gyroscope system about an input axis.
 2. Thesystem of claim 1, wherein the array of drive electrodes and the arrayof sense electrodes are each arranged longitudinally in the periodicpattern in respective orthogonal axes with respect to each other, andwherein the substantially matching array of drive electrodes and thesubstantially matching array of sense electrodes are each arrangedlongitudinally in the periodic pattern in respective orthogonal axeswith respect to each other.
 3. The system of claim 2, wherein thesubstantially planar vibrating-mass further comprises an array ofquadrature electrodes arranged at a 45° angle with respect to each ofthe sets of drive and sense electrodes, and wherein the housing furthercomprises a substantially matching array of quadrature electrodesarranged at a 45° angle with respect to each of the substantiallymatching sets of drive and sense electrodes, wherein the gyroscopecontroller is further configured to generate a quadrature signal that isprovided to one of the array of quadrature electrodes and thesubstantially matching array of quadrature electrodes to substantiallymitigate quadrature coupling into the force-rebalance signal.
 4. Thesystem of claim 1, wherein the substantially planar vibrating-masscomprises a first array of drive electrodes and a first array of senseelectrodes on the first surface and comprises a second array of driveelectrodes and a second array of sense electrodes on the second surface,and wherein the housing comprises a first substantially matching arrayof drive electrodes and a first substantially matching array of senseelectrodes respectively separated from and facing the first surface andcomprises a second substantially matching array of drive electrodes anda second substantially matching array of sense electrodes respectivelyseparated from and facing the second surface.
 5. The system of claim 1,wherein the drive signal is provided to the one of the array of driveelectrodes and the substantially matching array of drive electrodes toprovide for the in-plane periodic oscillatory motion of thesubstantially planar vibrating-mass in a direction that is orthogonalwith respect to a force that is generated in response to theforce-rebalance signal in response to rotation of the vibrating-massgyroscope system about the input axis.
 6. The system of claim 1, whereinthe sensor system comprises a plurality of substantially planarvibrating-masses arranged in pairs, each of the plurality ofsubstantially planar vibrating-masses comprising a first surface, asecond surface opposite the first surface, and a plurality of electrodesthat extend longitudinally in a periodic pattern across at least one ofthe first and second surfaces.
 7. The system of claim 6, wherein thegyroscope controller is configured to generate the drive signal toprovide for the in-plane periodic oscillatory motion of each of theplurality of substantially planar vibrating-masses in a manner that isout-of-phase by 180° with respect to a given pair, and wherein thegyroscope controller is configured to generate the force-rebalancesignal to generate a force in alternate and opposite directions for eachof the plurality of substantially planar vibrating-masses with respectto a given pair.
 8. The system of claim 1, wherein the plurality ofelectrodes further comprises an array of quadrature electrodes that arecapacitively coupled to a substantially matching array of quadratureelectrodes associated with the housing, the array of quadratureelectrodes being arranged at a 45° angle with respect to at least one ofthe sets of drive and sense electrodes and the substantially matchingarray of quadrature electrodes being arranged at a 45° angle withrespect to at least one of the substantially matching sets of drive andsense electrodes.
 9. The system of claim 8, wherein the gyroscopecontroller is configured to provide a DC quadrature signal to one of thearray of quadrature electrodes and the substantially matching array ofquadrature electrodes to substantially mitigate quadrature coupling intothe force-rebalance signal.
 10. The system of claim 1, wherein thevibrating-mass is coupled to the housing via at least one spring-masssystem, wherein the gyroscope controller is configured to generate acarrier signal having a frequency that is greater than a resonantfrequency of the at least one spring-mass system, wherein the drivesignal and the force-rebalance signal are generated at a frequency thatis approximately equal to the resonant frequency of the at least onespring-mass system based on demodulating pickoff signals associated withthe plurality of electrodes at the frequency of the carrier signal. 11.A method for calculating rotation about an input axis in avibrating-mass gyroscope system, the method comprising: monitoring adrive pickoff signal associated with one of an array of drive electrodesthat extend longitudinally in a periodic pattern across at least one ofa first surface and a second surface of a substantially planarvibrating-mass and a substantially matching array of drive electrodesthat extend longitudinally in a periodic pattern across at least one ofa first surface and a second surface of a housing, wherein the firstsurface of the substantially planar vibrating-mass faces the firstsurface of the housing and the second surface of the substantiallyplanar vibrating-mass faces the second surface of the housing; providinga drive signal to the one of the array of drive electrodes of thesubstantially planar vibrating-mass and the substantially matching arrayof drive electrodes of the housing based on the drive pickoff signal toprovide an in-plane periodic oscillatory motion of the substantiallyplanar vibrating-mass; monitoring a force-rebalance pickoff signalassociated with one of an array of sense electrodes that extendlongitudinally in a periodic pattern across at least one of the firstand second surfaces of the substantially planar vibrating-mass and asubstantially matching array of sense electrodes that extendlongitudinally in a periodic pattern across at least one of the firstand second surfaces of the housing; and providing a force-rebalancesignal to the one of the array of sense electrodes of the substantiallyplanar vibrating-mass and the substantially matching array of senseelectrodes of the housing based on the force-rebalance pickoff signal tocalculate a rotation of the vibrating-mass gyroscope system about aninput axis.
 12. The method of claim 11, wherein the array of driveelectrodes and the array of sense electrodes are each arrangedlongitudinally in the periodic pattern in respective orthogonal axeswith respect to each other across the at least one of the first andsecond surfaces of the respective substantially planar vibrating-massand the housing, and wherein the substantially matching array of driveelectrodes and the substantially matching array of sense electrodes areeach arranged longitudinally in the periodic pattern in respectiveorthogonal axes with respect to each other across the at least one ofthe first and second surfaces of the respective substantially planarvibrating-mass and the housing.
 13. The method of claim 11, furthercomprising: generating a DC quadrature signal; and providing the DCquadrature signal to one of an array of quadrature electrodes thatextend longitudinally in a periodic pattern across at least one of thefirst and second surfaces of the substantially planar vibrating-mass anda substantially matching array of sense electrodes that extendlongitudinally in a periodic pattern across at least one of the firstand second surfaces of the housing to substantially mitigate quadraturecoupling into the force-rebalance signal.
 14. The method of claim 13,wherein the array of quadrature electrodes are arranged at a 45° anglewith respect to at least one of the sets of drive and sense electrodes.15. The method of claim 11, wherein providing the drive signal comprisesproviding the drive signal to the one of the array of drive electrodesand the substantially matching array of drive electrodes to provide forthe in-plane periodic oscillatory motion of the substantially planarvibrating-mass in a first direction, and wherein providing theforce-rebalance signal comprises providing the force-rebalance signal tothe one of the array of sense electrodes and the substantially matchingarray of sense electrodes to provide a force that is generated inresponse to the force-rebalance signal in a second direction orthogonalto the first direction based rotation of the vibrating-mass gyroscopesystem about the input axis.
 16. The method of claim 11, whereinproviding the drive signal comprises providing the drive signal to theone of the array of drive electrodes and the substantially matchingarray of drive electrodes associated with a plurality of substantiallyplanar vibrating-masses arranged in pairs to provide for the in-planeperiodic oscillatory motion of each of the plurality of substantiallyplanar vibrating-masses that is out-of-phase by 180° with respect to agiven pair, and wherein providing the force-rebalance signal comprisesproviding the force-rebalance signal to the one of the array of senseelectrodes and the substantially matching array of sense electrodesassociated with the plurality of substantially planar vibrating-massesto provide a force in alternate and opposite directions with respect toa given pair.
 17. A vibrating-mass gyroscope system comprising: a sensorsystem comprising a plurality of substantially planar vibrating-massesthat each comprise a first surface, a second surface opposite the firstsurface, and a plurality of electrodes that extend longitudinally in aperiodic pattern across each of the first and second surfaces, theplurality of electrodes comprising an array of drive electrodes and anarray of sense electrodes that are capacitively coupled to asubstantially matching array of drive electrodes and a substantiallymatching array of sense electrodes, respectively, associated with ahousing and which are separated from and facing the respective at leastone of the first and second surfaces of each of the plurality ofvibrating-masses; and a gyroscope controller configured to generate adrive signal that is provided to one of the array of drive electrodesand the substantially matching array of drive electrodes associated witheach of the plurality of vibrating-masses to provide for an in-planeperiodic oscillatory motion of each of the plurality of substantiallyplanar vibrating-masses, and to generate a force-rebalance signal thatis provided to one of the array of sense electrodes and thesubstantially matching array of sense electrodes associated with each ofthe plurality of vibrating-masses to calculate a rotation of thevibrating-mass gyroscope system about an input axis.
 18. The system ofclaim 17, wherein the array of drive electrodes and the array of senseelectrodes associated with each of the plurality of vibrating-masses areeach arranged longitudinally in the periodic pattern in respectiveorthogonal axes with respect to each other on each of the first andsecond surfaces of each of the respective plurality of vibrating-masses,and wherein the substantially matching array of drive electrodes and thesubstantially matching array of sense electrodes on the housing andrespectively associated with each of the first and second surfaces ofeach of the plurality of substantially planar vibrating-masses are eacharranged longitudinally in the periodic pattern in respective orthogonalaxes with respect to each other.
 19. The system of claim 17, whereineach of the substantially planar vibrating-masses further comprises anarray of quadrature electrodes on each of the first and second surfacesand which are arranged at a 45° angle with respect to each of the setsof drive and sense electrodes, and wherein the housing further comprisesa substantially matching array of quadrature electrodes associated witheach of the first and second surfaces of each of the plurality ofsubstantially planar vibrating-masses and which are arranged at a 45°angle with respect to each of the substantially matching sets of driveand sense electrodes, wherein the gyroscope controller is furtherconfigured to generate a quadrature signal that is provided to one ofthe array of quadrature electrodes and the substantially matching arrayof quadrature electrodes associated with each of the plurality ofsubstantially planar vibrating-masses to substantially mitigatequadrature coupling into the force-rebalance signal.
 20. The system ofclaim 17, wherein the plurality of substantially planar vibrating-massesare arranged in pairs, wherein the gyroscope controller is configured togenerate the drive signal to provide for the in-plane periodicoscillatory motion of each of the plurality of substantially planarvibrating-masses in a manner that is out-of-phase by 180° with respectto a given pair, and wherein the gyroscope controller is configured togenerate the force-rebalance signal to generate a force in alternate andopposite directions for each of the plurality of substantially planarvibrating-masses with respect to a given pair.